A polyhedral approach for the Equitable Coloring Problem

TL;DR

This paper investigates the polytope related to the Equitable Coloring Problem, identifying valid inequalities and conditions for facet-defining inequalities, and demonstrates their effectiveness through computational experiments.

Contribution

It introduces new families of valid inequalities and conditions for facet-defining inequalities in the polytope of the problem, enhancing solution methods.

Findings

Identified several families of valid inequalities.

Derived sufficient conditions for facet-defining inequalities.

Computational evidence shows improved algorithm performance.

Abstract

In this work we study the polytope associated with a 0,1-integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining inequalities. We also present computational evidence that shows the efficacy of these inequalities used in a cutting-plane algorithm.